Resolution and Field of View

A Self-Centered, Short-Sighted Analysis of VLST

Possibilities

Gary Bernstein

University of Pennsylvania

2/27/04

Why Build a Big Telescope?

• Collecting area – Replicable with multiple apertures.

• Resolution– Replicable with unfilled aperture.

€

A∝D2

€

θ ∝λ /D

What good is resolution?

• Morphological information, e.g. high-z galaxy substructure, circumstellar disks.

• Confused regions, e.g. stellar pops beyond M31, MBH’s at galaxy centers, high-contrast studies.

• Improved S/N for unresolved, sky-limited sources.

When does resolution improve observing speed?

•Exposure times for broadband S/N=10 point sources, with λ/D pixel size.

•Sky limit for V>29 on 2.5m, V>32 on 10m!

•Same for spectroscopy.

•Even fainter at λ<500 nm

•Exposure time to reach sky-limited point is always about 1 hour.

10m resolution is useless for uncrowded V<29!

When does resolution improve observing speed?

•Longest exposures near 100 hours for HST, Chandra.

•Plot shows limit for S/N>10 point sources (500 nm) vs resolution, on 10-meter VLST.

•High-res spectra will never be in sky-limited regime of the 2.5-m telescope.

•Multiple apertures just as good as one large telescope!

•Need lower detector noise for multiple apertures though.

When does resolution improve observing speed?

•Advantage of single aperture kicks in between 29<V<32.

•Only for sources <10 mas (at 500 nm)

Figures of Merit for VLST designs

•Single targets with size>40 mas or V<29: speed A; multiple apertures equivalent to large aperture.

•Unresolved/crowded single targets V>29: speed A/ large aperture is advantageous (AO?).

•Searches or sky-filling targets resolved or V<29: speed A

•Searches or sky-filling targets unresolved & V>29: speed A/

How Does FOV scale with aperture?•Simple geometric similarity shows that FOV is independent of D if we will accept fixed-angular-size geometric aberrations.

•But note that the physical area of detector required scales as D2 A. Fixed-scale pixels will have fixed Npix but large cosmic-ray rate. Fixed-size pixels have Npix D2

•Here A just scales as total collecting area, and required detector area is also independent of multiple- vs single-aperture choice!

•If we want to keep aberrations below the diffraction scale, then the FOV must shrink. Three-mirror telescopes have leading aberrations θ5, so D-0.4.

•Now A D1.6 Npix. Total throughput is dependent on total pixel count, which is higher per unit aperture in multiple-aperture scheme.

•But A D3.6, so sky-limited target surveys prefer single aperture.

What about a Multiple-Aperture Telescope?•Equal to single-aperture telescope of same total area when A or A is figure of merit.

•Cost per square meter is lower (?)

•Required detector real estate is equivalent.

•Much more compact structure stiffer, easier to hold figure, higher resonant frequencies, faster slews and settling.

•More robust because of risk-spreading.

•More flexible scheduling, can target telescopes independently.

•Faster response

•Can specialize units of the fleet, e.g. a wider filter choice available.

•Already know how to build these, just need them to be cheaper.

•No need to train squad of L2 android astronomers to assemble.

•Element cycling is natural path to decade-scale upgrades.

•Easier to get wide-field multi-object spectroscopy.

Self-centered Science Example: KBOs

VLST Opportunities for KBOs

•Large samples of V<29 (15 km) KBOs; how does the accretion process depend on dynamical state?

•This investigation prefers multiple-aperture VLST.

•Directly detect the precursors of comets to V≈34.

•Would seem to prefer single-aperture telescope, BUT the dispersion of KBO apparent motions exceeds 10 mas in 30 seconds even in favorable conditions, so enormous bandwidth & computing required to use such high resolution.

•Targetted followup: high resolution (or interferometry) for angular sizes; colors, light curves, etc.

Weak Gravitational Lensing with VLST•Now apparent that weak lensing sky holds a vast amount of information:

•Time history of the dark energy equation of state.

•Masses of the neutrinos.

•Slope/running index of inflationary spectrum.

•Is the WMAP CMB low-l deficit a fluke?

•How do dark halo properties connect with visible galaxy properties?

•Figures of merit for WL observations:

•Number of resolved galaxies per arcmin2

•Fraction of sky covered by survey

Instrument Requirements for Weak Lensing

•HDF, etc., have very few unresolved galaxies! Additional resolution below 50 mas does not greatly increase WL information.

•Deeper images gain galaxies only slowly once we are looking at L* galaxies at Ly break. Helps WL only at small angular scales.

•Want to scan as much of sky as possible, good photo-z’s, with HST-ish resolution, so A is the figure of merit for space observatories.

•Multiple-aperture approach seems ideal here.

Something to think about…An space-based Vis/NIR survey of the full sky seems inevitable - why not start thinking about it? [Note: full sky 10 bands 0.05” pix=2x1015 pixels!]

SPace All Sky Multiband Survey (SPASMS)

Constellation V?MultiSNAP? Astrono-MIRV?

Survey/Instrumen

t

A(m2

deg2)

Npix Galaxy Density (arcmin-

2)

Fsky

Cosmos/ACS

0.016 16Mpix 70?0.00005/0.12 yr

NIRCam/JWST

0.05 16 Mpix

LSST230 1 Gpix 30

0.5/10 yr

SNAP/Wide

2.2 0.5 Gpix 100+0.025/1 yr

VLST/SPASMS 55 13 Gpix 100+

1/2 yrs

WL Capabilities of Observatories

Summary

•Much VLST science will demand 10-meter diffraction-limited resolution of morphology and crowding. Think about AO, unfilled-aperture alternatives for some of this.

•But for many survey projects and any high-resolution spectroscopy, a more attractive solution might be to spread the aperture over ~20 telescopes.

•SPASM survey would take 2 years and yield stunning ultimate weak lensing results, nearly full inventory of Galactic stars, all >10 km planetesimals in Solar System, and an extremely flexible observatory.